Create one curve object per spline in Animation Nodes?
Animation Nodes have a node called Trim Spline Node which can be used to dynamically trim splines. There are certain complications, however, if one decided to use this node:


Edges are not directed, so you may observe some splines growing outward from a vertex and other splines inward toward a vertex.
There no easy way to determine which edges belong to which vertex, in other words, there is no way to determine the locations of the points of the spline to derive the trim node by.


Thus we are forced to to use a more advanced approach, but no worries, it is just as easy.

First, we loop over edges, get the vertices locations at the indices of the edge indices, sort the vertices in the direction of the animation, I can see that your animation is from the left to right, so we check if the $x$ location of the first vertex is larger than that of the second, if it is, we reverse the list such that the first vertex becomes the one that is closest to the initial location of the animated effector, then we create a spline from those vertices.



Second, we trim the output splines based on the distance between the effector and the initial vertex of the spline, since your animation is along the $x$ axis, the distance is simply the difference between the $x$ locations of the effector and the vertex:



Which results in:



Notice that the trim node shouldn't be used here, because the spline is just a line so a linear combination between both vertices of the line would yield the same effect, but I just wanted to show you how trim node can be used.